What is the difference between continuous domains and discrete combinatorial optimization?
A continous domain can be imagined as a space in which the axes of the coordinate systems are the parameters of the continous domain. If we take 2D Cartesian space as an example, it is a continous domain where there is an infininite amount of possibilities of placing an object in this space. Let's call the position of the object its state. Constraining the space to e.g. a sheet of paper does not change its continuity. There is still an infinte amount of posibilites of placing a dot (or any object) on that sheet of paper or with other words the state space of the dot is still infietly large. 

Computational methods are much better in dealing with descretet spaces (mainly because the possiblities to take the next step is limited). In a discrete space the possibilities are limited. If we take the example above and discretize the sheet of paper, e.g. use a grid on the paper and say that we are not interested in the exact location of the point, just in which grid it is in we have succesfully defined a discrete space. 

A different example for a problem in descrete domain can be navigation on a map. If we assume that the exact rajectory is not important, then we can make descrete decisions of turning left, right or moving forwards or backwards by one step. Even if add further possibilites (like moving up one step or down) until the number of possibilities in one state is not infinite the domain is descret.